Achieving Distributed Convex Optimization Within Prescribed Time for High-Order Nonlinear Multiagent Systems
针对高阶非线性多智能体系统，提出一种级联设计框架，将分布式凸优化问题转化为预设时间稳定问题，并给出稳定性判据，适用于有干扰或参数不确定的系统。
This article addresses the distributed prescribed-time convex optimization (DPTCO) problem for high-order nonlinear multiagent systems (MASs) under undirected connected graphs. A cascade design framework is proposed that divides the DPTCO implementation into distributed optimal trajectory generator design and local reference trajectory tracking controller design. The DPTCO problem is then transformed into the prescribed-time stabilization problem of a cascaded system. Using changing Lyapunov functions and time-varying state transformations with sufficient conditions, we establish criteria for prescribed-time stabilization and prove the boundedness of internal signals in closed-loop MASs. The framework addresses robust DPTCO for chain-integrator MASs with disturbances through the introduction of novel sliding-mode variables and time-varying gains. It also solves adaptive DPTCO for strict-feedback MASs with parameter uncertainty via backstepping method and descending power state transformation. Two numerical examples verify the theoretical results.